Răspuns
Explicație pas cu pas:
a) x*y = xy -2x - 2y + 4 + 2 = x(y-2) - 2(y-2) + 2 =
(y-2)(x-2) + 2. Q.E.D.
b) x*2x = (x-2)(2x-2) + 2 = 14
2(x-2)(x-1) = 12
(x-2)(x-1) = 6 = ca produs de doi factori consecutivi, deci avem
1) -3 si -2, deci x1 = -1
sau
2) 2 si 3, deci x2 = 4.
c) 1*2*3* ... * 99 * 100 = [(1-2)(2-2) + 2] *3*4*...*100 =
2*3*4*...*100 = (0*1 + 2) * 4 * ... *100 =
2*4*...*100 =
......
2*5...*100 =
.......
2*100 =
2
